MATH GAMES THAT CONNECT
UNDERSTANDING TO LEARNING
JOHN FELLING
ASCD ANAHEIM
MARCH 25-27, 2017
[email protected]
phone 1-866-342-3386
1-780-440-6284
boxcarsandoneeyedjacks.com
BoxCarsEduc
BoxcarsEducation
For electronic copy send an email to:
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Please include the
conference/workshop title
BETWEENERS
LEVEL:
Grade 3 - 4
CONCEPTS:
ordering whole numbers and decimals, analytical thinking
PLAYERS:
3 or 4
EQUIPMENT:
1 x 3-in-a-cube die per player, 1 recording sheet per player
GOAL:
to have a between number in each round
GETTING STARTED:
To begin, each player records the names of all the players in the round on their recording sheets. All players
shake their 3-in-a-cube die. On STOP players peek at their die, mentally figure all possible 3-digit numbers
they can make from their roll and then record one of the possibilities next to their name on their recording
sheet. Players then announce their numbers and record every player's number next to that player's name
on their gameboard. Players compare all the recorded numbers in the round.
EXAMPLE:
STRATEGIZING...
math
thinking
Player
John: "456 is the least
I can make but has
the best chance to be
the between number
for the round."
math
thinking
Roll
Number
John
4,5,6
456
Jane
1,2,3
321
Norm
1,4,5
415
math
thinking
Jane: "321 is the
greatest I can make but
has the best chance to
be the between number
for the round."
Norm: "541 is too large to win,
145 is too small to win, my best
chance is either 451 or 415. 415
is closer to the middle and is my
best chance to be the between
number.
t
rule
w
ist
"John's 456 is greatest. Jane's 321 is least. Norm's 415 is between 321 and 456." Players circle 415
and Norm earns a point for the round.
1. Four Player Version - Rules and scoring remain the same, however there can be two
between numbers in a round, with two players earning points if their numbers fall between
the greatest and least for the round.
2. Students must place a decimal point in their number (eg roll 4,6,1 - 46.1, 4.61, .461)
Rules and scoring remain the same.
©Box Cars and One-Eyed Jacks
2
BETWEENERS
primary
1. Players must make the largest number they can with their roll. They compare their numbers and the
BETWEEN number wins a point.
2. Players roll one 10 sided double dice and play a 10's and 1's version. Players must decide which die
(inside or outside) will represent the 10's and 1's place. Rules and scoring remain the same.
middle
years
1. Players use their three numbers in a math sentence with the goal of having their answer being
between the answers of their opponents.
EXAMPLE:
Player
math
thinking
Roll
Number
John
4,5,6
5 × (6 - 4) = 10
Jane
1,2,3
(2 + 1) × 3 = 9
Norm
1,4,5
5+4-1=8
John: "What makes a good BETWEEN answer? I'm
thinking something between 8 and 15."
math
thinking
scores 1 point
Jane: "3, 2 and 1 are small numbers so I need
to maximize the answer I can get with them."
math
thinking
Norm: "Answers around 7 or 8 have been winners in the
past few rounds so I want an answer close to those."
math talk
John: " I first subtracted 4 from 6 so I had to place that in parentheses. I then multiplied
the difference of (6-4) by 5 to get an answer of 10."
Jane: "I placed 2+1 in parentheses because I wanted to have that done first so I could
multiply the sum of (2+1) by 3 to give me a product of 9 for an answer."
Norm: "I added 5+4 to get 9 then subtracted the 1 to get a final answer of 8."
Jane scores 1 point for having the "between answer".
JOURNAL WORK & EXTENSIONS:
1. Explain what would be the ideal between number if you used two 10-sided double dice?
©Box Cars and One-Eyed Jacks
3
BETWEENERS & CUBIC MYSTERY
PLAYER
ROLL
PLAYER
RECORDING SHEET
NUMBER
PLAYER
ROLL
NUMBER
ROLL
NUMBER
PLAYER
ROLL
NUMBER
PLAYER
ROLL
NUMBER
PLAYER
ROLL
NUMBER
PLAYER
ROLL
NUMBER
PLAYER
ROLL
NUMBER
©Box Cars and One-Eyed Jacks
4
Rounding Recording Sheet
Turn
Rolled
Standard
Rounded
To 10's
Rounded
to 100's
example
400 , 20 , 7
427
430
400
Notes
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
© Box Cars And One Eyed Jacks 2014
5
10 SIDED DOUBLE DICE WARM UPS
1. ADDITION: SUMS TO 18 - each player rolls a 10-sided double dice and adds their sum. Both players
verbalize their sum. The player with the greatest sum scores a point.
6
8
= 15
9
"15 is a greater sum than 11"
= 11
3
Students can explore the commutative property of addition: 6 + 9 = 15 or 9 + 6 = 15"
2. ADDITION: SUMS TO 36 WITH REGROUPING - each player rolls two 10-sided double dice and adds
all four addends for the greatest sum. The player with the greatest sum scores a point.
Player One:
6
2
+
9
5
Player Two:
= 8 + 14 = 22
9
4
+
6
2
= 13 + 8 = 21
"22 is a greater sum than 21"
This is a great activity for students to explore the associative property of addition. Addends from
Player One above: 6 2 9 5
= 11 + 11 = 22
3. ADDITION: DOUBLES TO 36 - this is a two step mental math activity. Each player rolls a 10-sided
double die, adds their sum, and then doubles it. The player with the greatest doubled sum scores a
point.
Player One:
Player Two:
6
=6+4
10 x 2 = 20
4
9
=9+5
14 x 2 = 28
5
"28 is a greater sum than 20"
4. SUBTRACTION: FROM 9 - each player rolls a 10-sided double die, and subtracts the numbers for the
least difference. The player with the least difference scores a point.
Player One:
9
Player Two:
=9-8=1
8
6
=6-2=4
2
"1 is a smaller difference than 4"
©Box Cars and One-Eyed Jacks
6
10 SIDED DOUBLE DICE WARM UPS
5. PLACE VALUE TO 99 - Outside number is 10's value, inside number is the unit or "one's". Students
should play on a number line and place their die right down onto it to compare numbers.
Play for greatest number, in later practice sessions work on least.
Player One:
2
Player Two:
"9 tens 2 ones = ninety-two"
92
9
4
6
"6 tens 4 ones = sixty-four"
64
"92 is greater than 64"
As students mature, they can estimate and verbalize the difference between the two numbers:
"92 is about 30 more than 64"
=10
is ≈10
Add a third player and the between value scores a point.
t
w
ist
=10
rule
92
84
74
Player One:
1
8
Player Two:
81
1
1
Player Three:
11
11
Player Two
3
6
63
63
81
Player Three
Player one
"63 is between 11 and 81, Player Three scores a point"
6. DECIMAL PLACE VALUE
©Box Cars and One-Eyed Jacks
7
10 SIDED DOUBLE DICE WARM UPS
7. MULTIPLICATION: PRODUCTS TO 81 including practice with 0 - each player rolls a 10-sided double
die and multiplies the two factors. The player with the greatest product scores a point.
6
2
6 x 9 = 54
9
2x0=0
0
Students can explore the commutative property of multiplication in this activity: "6 x 9 = 54 ; 9 x 6 = 54"
8. EQUIVALENT FRACTIONS - players roll one 10-sided double die between them and write down the
fraction less than one that can be made. If 0 is rolled, it is used as "tenths" 10 . The players call out a
simplified fraction (if possible) and one other fraction name.
Play cooperatively.
3
6
=
3
6
=
1
2
and
6
12
©Box Cars and One-Eyed Jacks
5
7
=
10
14
8
Multiplication Estimation – Recording Sheet
Name: _______________________ Date: ________________
Round
Rolls
Estimate
Actual
Difference
Example
17 X 23
380
391
10
1
X
2
X
3
X
4
X
5
X
6
X
7
X
8
X
9
X
10
X
11
X
12
X
Total Differences =
©Box Cars and One-Eyed Jacks
9
MATH SHAKERS
©Box Cars and One-Eyed Jacks
10
A
H
B
FLUENCY PRACTICE
+ STRATEGIES
+ WHOLE BRAIN ENGAGEMENT
= POWERFUL LEARNING
A
RE
A
E
V
M AT H S H A KE
K
Subitizing, recognizing numbers 1-6
Comparing > <, numbers 1-6, ODD/EVEN
Recognition of doubles, doubles + 1
Plus 1, Plus 2, Minus 1, Minus 2
Making 10’s, 100’s, Rounding
Addition to 12 Commutative; Adding to 18 Associative
Addition with multi-digit numbers, estimation
Multiplication to 36 Commutative, Multiplication Associative
Place Value - reading numbers from ten’s ► 1,000,000
Reading decimals
Comparing number > < 10’s ► 1,000,000
Fractions - less than one, greater than one and fractions = 1
©Box Cars and One-Eyed Jacks
11
MAKE A TEN SHAKERS
LEVEL:
Kindergarten - Grade 2
SKILL:
fact fluency, subitizing, making a sum of 10
SET UP:
vertical or horizontal, 1 die in each slot, 1 shaker for 2 students
PLAYERS:
2 (cooperative pair) or solitaire
GOAL:
call out number, immediately give missing addend to equal a sum
of 10
GETTING STARTED:
For solitaire or pair work have students shake a container, hold it still, then say out loud
their numbers as they work down the slots:
SEE
SAY
SEE
math talk
SAY
“4”
+6
“10”
“3”
+7
“10”
+7
“10”
“3”
“6”
Have students
then go back
through, working
from the top,
giving the
missing addend
to equal 10.
math talk
+4
“10”
+9
“10”
“2”
+8
“10”
“4”
+6
“10”
“1”
Have students work
toward full fluency,
see say
“4 + 6 = 10”
Have students record their "ten facts" using the recording sheets when ready.
©Box Cars and One-Eyed Jacks
12
MAKE A TEN SHAKERS RECORDING SHEET
SEE +
SEE +
?
?
SEE +
?
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
SEE +
SEE +
?
?
SEE +
?
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
+
=
10
©Box Cars and One-Eyed Jacks
13
FRACTION ACTION
LEVEL:
Grade 3-6
SKILL:
identifying and naming proper fractions, improper fractions,
fractions equal to 1
SET UP:
horizontal, 1 die in each slot (preferably 2 different colors of
dice), 2 shakers
PLAYERS:
3
GOAL:
to have the most points after nine rounds
GETTING STARTED:
Players will play 3 sets of 3 rounds each. In the first round, Player One will be assigned
to look for proper fractions, Player Two will be assigned to look for improper fractions,
and Player Three will look for fractions that equal 1.
Players shake the two containers until STOP is called and the containers are then lined up
to create 7 fractions.
EXAMPLE:
(Round One)
Numerator
Denominator
3
=1
3
1
4
2
=1
2
4
=2
2
1
5
2
3
5
2
=1
3
3
Players now analyze the types of fractions rolled and score 1 point for each falling within
their category.
1
1
2
3 points
Player One scores 1 point for each proper fraction: 4
5
3
Player Two scores 1 point for each improper fraction:
4
=2
2
5
2
=1
3
3
Player Three scores 1 point for each fraction that equals 1: 3 = 1
3
2
=1
2
2 points
2 points
Player One wins this Shaking Round!
©Box Cars and One-Eyed Jacks
14
FRACTION ACTION
For the second round, players will rotate the type of fraction they are looking for (ie
Player Two will be assigned to look for proper fractions, Player Three will be assigned
to look for improper fractions, and Player One will look for fractions that equal 1) and
then shake the containers again to create seven new fractions. Students analyze this new
shake and score accordingly. For the final round in the set, players once again rotate the
type of fractions they are looking for, (ie Player Three will be assigned to look for proper
fractions, Player One will be assigned to look for improper fractions, and Player Two
will look for fractions that equal 1) and shake for a third round, creating new fractions
and scoring accordingly. Continue play with 2 more sets of 3 rounds, rotating the type
of fractions as per the first set. The player with the most points after 9 rounds is the
winner.
FOLLOW UP ACTIVITIES:
1. Have students record each round and arrange their fractions from least to greatest on
the recording sheet.
1
5
1
4
2
3
2
2
3
3
2. Have students circle
all proper fractions, box
cloud all fractions that equal one.
5
3
4
2
all improper fractions and
3. Have students see which improper fractions can be simplified to mixed fractions. For
example
5
3
2
simplifies to 1 3 .
4. Have students plot every other round on an open number line.
math
thinking
5. Have students explore if the game would be fair if the type of fraction
they were looking for did not change with each round. Have students explain their
thinking by drawing all possible outcomes.
©Box Cars and One-Eyed Jacks
15
FRACTION ACTION RECORDING SHEET
SET ONE
ROUND 1
ROUND 2
ROUND 3
numerator
denominator
numerator
denominator
numerator
denominator
SET TWO
ROUND 4
ROUND 5
ROUND 6
numerator
denominator
numerator
denominator
numerator
denominator
SET THREE
ROUND 7
ROUND 8
ROUND 9
numerator
denominator
numerator
denominator
numerator
denominator
©Box Cars and One-Eyed Jacks
16
FRACTION ACTION RECORDING SHEET
SHAKE 1
SHAKE 2
SHAKE 3
SHAKE 4
SHAKE 5
SHAKE 6
SHAKE 7
SHAKE 8
SHAKE 9
SHAKE 10
numerator
denominator
numerator
denominator
numerator
denominator
numerator
denominator
numerator
denominator
numerator
denominator
numerator
denominator
numerator
denominator
numerator
denominator
numerator
denominator
©Box Cars and One-Eyed Jacks
17
ROCK AND ROLL
LEVEL:
3-6
SKILLS:
comparing place value, expanding numbers
PLAYERS:
2 – 4 (1 player as referee)
EQUIPMENT:
GOAL:
2 – 6 dice per player (# of dice determines size of number), recording sheet
to be the first player to order their dice and to create the greatest number possible
GETTING STARTED:
The referee calls players to “Rock and Roll”. All players shake their dice and hide the roll with their
hands until the referee calls “Reveal”. Players then begin arranging their dice to make the largest
number possible. The first player to finish calls out “Rock and Roll”. All other players must
immediately freeze their work in their current order and pull their hands off their dice. The first player
verbalizes their number to the other players.
If the first player to finish has correctly ordered and read their number, they earn 5 points. If they are
also the largest number of the group they earn another 5 points for a total of 10 points. All other
players earn zero. If any player in the group has a number greater than the first to call “Rock and
Roll” they earn 5 points for the round as well.
MATH TALK
Don’t let students use AND when reading their numbers. AND is the decimal.
EXAMPLE:
Playing to ten thousands
ROLL:
ARRANGE:
5
READ:
5
,
4
2
1
Fifty-five thousand, four hundred twenty-one
©Box Cars and One-Eyed Jacks
18
ROCK AND ROLL
VARIATIONS:
1. Students play for the least possible number.
2. Students play on the decimal game sheet.
3. Arrange and write all your numbers in ascending order.
MATH JOURNAL WORK AND EXTENSIONS:
1. Why is it important to see place value represented in many different ways?
2. What is the largest possible number that can be rolled? The least? How close were you on
any roll to either of these possibilities?
3. What strategy did you use to tell which number is greatest in the round? Do you use the same
strategy when the numbers are very close?
4. This game is excellent for teaching expanded notation. After each round have players slot
their dice into the black tray on top of the Stratedice place value chart. This provides the
language for the students.
After the dice are slotted in, have players expand them out as follows:
<<SAMPLE>>
The blank spaces in the trays represent zeroes. Students can put their fingers right into the
empty slots. From this physical expanding of the number we then have students record on
their math journal recording sheet.
©Box Cars and One-Eyed Jacks
19
ROCK AND ROLL
RECORDING SHEET
ROLL
NUMBER
EXPANDED NUMBER
1
2
3
4
5
6
7
8
9
10
11
12
13
14
©Box Cars and One-Eyed Jacks
20
©Box Cars and One-Eyed Jacks
ONES
TENS
HUNDREDS
THOUSANDS
TEN THOUSANDS
HUNDRED THOUSANDS
ROCK AND ROLL
21
HORSE RACE – PRIMARY ADDITION
LEVEL:
K-2
SKILLS:
adding to 12, commutative property of addition, fact families
PLAYERS:
2 (1 vs 1)
EQUIPMENT:
GOAL:
tray of dice (each player needs 18 of their own color), gameboard
to have the greatest number of dice on your side of the “racetrack” at the end of the game
GETTING STARTED:
Each player takes 18 dice of one color and picks a side of the dice tray to be their “racetrack”. Each
player picks up a pair of dice, rolls, and calculates their sum. The player with the greatest sum puts
their dice into their side of the racetrack. Both players verbalize their sums.
EXAMPLE:
+
=
PLAYER ONE
MATH TALK
8
+
=
6
PLAYER TWO
Player One says “8 is a greater sum than 6”
The player with the greatest sum places their dice in their side of the racetrack. The player with the
least sum tosses their dice into the lid.
Players each pick up another pair of dice, roll and compare their next sums. In the event of a
EQUAL SUM – both players put their two dice into their side of the racetrack.
TIE
or
Play continues until both players’ 18 dice have been rolled out. The player with the greatest number
of dice on their side of the racetrack wins.
MATH JOURNAL WORK AND EXTENSIONS:
This game is full of opportunities to teach basic addition concepts, adding to 12.
1. Have players record a full game on the recording sheet. See example on page 56.
2. Have players highlight or color in examples of doubles, near doubles. Count how many were
rolled in your game, and compare with the rest of the class.
3. As students are playing, observe the following:
• Which students are identifying sums immediately?
• Which students are counting on from the greatest addend? Least addend?
• Which students are recognizing the doubles and doubles +1 and using these to add
quickly or with immediate recall?
©Box Cars and One-Eyed Jacks
22
HORSE RACE – PRIMARY ADDITION
•
Which students are still at a concrete level of touching the pips on the dice, and will
need more practice with immediate recognition of patterns to 6?
4. As a class you can analyze the types of games that happened. When a game is complete, we
have students determine if their Horse Race was: (see example on bottom corner of p. 56)
• Dead Heat – both players have the exact same amount of dice on their trays
• Wipe Out – one player has at least 3 or more pairs greater in their side of the
racetrack
• Too Close to Call – basically the game is close throughout the play and is typically
won by one or two pairs, right near the end of the game
5. You can also analyze as a class the following questions:
• How many doubles were rolled in the game? Keep track by tallying or taking
counters each time doubles are rolled.
• How many tie sums were rolled in your game? Compare your total with the rest of
the class. How many of your tie sums were identical rolls? For example:
•
tie sums
4+4=8
6+2=8
tie sums with identical rolls
3+3=6
3+3=6
PLAYER ONE
PLAYER TWO
This analysis helps students understand fact families, and that some sums have
more than one roll or pair of addends that equal it.
Which sums often had ties?
6. Have students work with the commutative property of addition which states:
“The sum stays the same when the order of the addends is changed.”
6 +4
=
4+6
+
=
+
We have the students cover up one addend with their hand and verbalize:
4
+ 6 = 10
6
©Box Cars and One-Eyed Jacks
+ 4 = 10
23
HORSE RACE – PRIMARY ADDITION
PLAYER
ONE
BOTH
PLAYERS
START
PLAYER
TWO
START
©Box Cars and One-Eyed Jacks
24
Horse Race - Graphing, Interpreting, Inferring
Box Cars and One-Eyed Jacks ©2015
Set Up
Play the game Horse Race (one player uses white dice, one player uses blue dice), it is extremely important
that the players place the dice properly in the tray or lid. In other words, if a player rolls a 2 and a 3, then
they must put 2 and 3 into the tray or lid (not just toss them in so any value faces up). Versions of Horse
Race for this activity include: 2 addend addition (largest sum wins), 3 addend addition (largest sum wins),
single digit subtraction (smallest difference wins), 2 factor multiplication (largest product wins), 3 factor
multiplication (largest product wins), comparing proper fractions (smallest value wins).
Once the players have completed their game, they evaluate their game to determine whether it was a tie or
who won (blue or white). Also, for win/loss games, they evaluate whether the win was close or a "blow
out" (one player won by a lot). Players can also quickly estimate (ie not count exactly) what dice values
(regardless of color) were rolled the most/least.
Graphing, Interpreting and Inferring
Players take all of the dice from both the tray and the lid and create a bar graph by lining up the dice
according to their value. From this graph they can easily see which number(s) were rolled the most/least
and may be able to determine the likely winner (white or blue).
STEP 2: Reorganize Dice to Create a
Double Bar Graph
STEP 1: Create Single Bar Graph
As a further extension, students can alter the graph by lining up the blue and white dice for each value next
to each other to create a double-bar graph. Students can then write on a sticky note which color won and
whether the win was close or a blow out. Students visit other games and with only looking at the doublebar graph try to figure by discussing the graphs with their own partners, whether the game was won by
blue or white and whether it was close or a blow out.
Math Journal Questions
1. How did you infer which color won or if the game ended in a tie?
2. How did you infer whether win/loss games ended as a close race or blow out?
3. Were your inferences always correct?
4. What types of games were easiest to infer correctly, hardest to infer correctly and explain why you
think they were easy or hard to infer correctly.
©Box Cars and One-Eyed Jacks
25
Let The Games Begin
All the Box Cars games are written using the same format. As a sample, we've
chosen one of our basic games to familiarize you with our style.
LEVEL:
SKILLS:
PLAYERS:
EQUIPMENT:
GETTING STARTED:
Cards 1 - 5
Cards 1 - 9
Grade 1 - 7
addition facts 1 - 10, 1 - 18 combinations
2
Cards (Ace = 1) - 5, or (Ace = 1) - 9
Players divide cards evenly between themselves. Each player
turns over two cards and adds them together. The highest sum gets all the
cards. In the event of a tie; (ie: each player has the same sum), WAR is
declared. Each player deals out three more cards face down and then
turns over two more cards. These two cards are added together. The
highest sum wins all of the cars. Play continues until one player has
collected all of the cards.
Grade 1 - 2 Sums to 10
Grade 2 - 3 Sums to 18
Player 1
Player 2
2+3
4+1
War is declared
2+3
4+1
Concepts: Missing Addend, Factor
Equipment: Cards 0-12 (J=11 Q=12 K=0)
Goal/Object: Figure Out value of the card on
your head
3 cards are turned
upside down.
4+3
Salute
Box Cars "All Hands On Deck" Mystery Number (adapted)
6+2
Player 2 collects all of the cards Try
These Variations Place
Usually 3 players with one player taking the role
of "General". The General says "salute". The
other two players take the card from the top of
their deck and WITHOUT LOOKING AT IT place
it on their forehead so everyone else can see
what the card on their forehead is. The General
Adds the two cards together and says "The sum
of your two cards is...." The two players then
Value War
Subtraction War
3 Addend War
Multiplication War
Integer War Fraction
War
Mixed Operations
use the sum and the card they can see on their
opponent's forehead to try and figure out their
own card.
Variations: (1) Multiplication (take out 0s)
(2) 4 Players (one General, 3 soldiers)
(3) Red = neg integers / Black = pos integers
Remember: War is a traditional game.
However, due to the negative connotation
you may want to change the term "war'' to
one of your own choice.
We often call these our Buzz Games (ie.
Three Card Buzz).
©Box Cars and One-Eyed Jacks
26